What is (\partial)/(\partial x)(x/(x^2+2y^2)+3x) ?

The answer to (\partial)/(\partial x)(x/(x^2+2y^2)+3x) is (-x^2+2y^2)/((x^2+2y^2)^2)+3

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(\partial)/(\partial x)(x/(x^2+2y^2)+3x)

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 2 y ^{2}} + 3 x)

\frac{- x ^{2} + 2 y ^{2}}{( x ^{2} + 2 y ^{2} ) ^{2}} + 3

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 2 y ^{2}} + 3 x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (\frac{x}{x ^{2} + 2 y ^{2}}) + \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 2 y ^{2}}) = \frac{- x ^{2} + 2 y ^{2}}{( x ^{2} + 2 y ^{2} ) ^{2}}

\frac{\partial}{\partial x} (3 x) = 3

= \frac{- x ^{2} + 2 y ^{2}}{( x ^{2} + 2 y ^{2} ) ^{2}} + 3

x \to 1 lim (2 ∣ x - 1 ∣ - 1)

a y^{^{''}} + b y = 0

sin (\frac{π x}{2})

2 sin (3 x)

\int \frac{sin ( \frac{1}{x ^{3}} )}{x ^{4}} d x

What is (\partial)/(\partial x)(x/(x^2+2y^2)+3x) ?
The answer to (\partial)/(\partial x)(x/(x^2+2y^2)+3x) is (-x^2+2y^2)/((x^2+2y^2)^2)+3